{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<small><i>This notebook was put together by [Jake Vanderplas](http://www.vanderplas.com). Source and license info is on [GitHub](https://github.com/jakevdp/sklearn_tutorial/).</i></small>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Supervised Learning In-Depth: Support Vector Machines"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Previously we introduced supervised machine learning.\n",
    "There are many supervised learning algorithms available; here we'll go into brief detail one of the most powerful and interesting methods: **Support Vector Machines (SVMs)**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import stats\n",
    "\n",
    "plt.style.use('seaborn')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Motivating Support Vector Machines"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Support Vector Machines (SVMs) are a powerful supervised learning algorithm used for **classification** or for **regression**. SVMs are a **discriminative** classifier: that is, they draw a boundary between clusters of data.\n",
    "\n",
    "Let's show a quick example of support vector classification. First we need to create a dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAdkAAAFJCAYAAADXIVdBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nXjyhBaY1AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x396 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets.samples_generator import make_blobs\n",
    "X, y = make_blobs(n_samples=50, centers=2,\n",
    "                  random_state=0, cluster_std=0.60)\n",
    "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A discriminative classifier attempts to draw a line between the two sets of data. Immediately we see a problem: such a line is ill-posed! For example, we could come up with several possibilities which perfectly discriminate between the classes in this example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeAAAAFJCAYAAABDx/6zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nEMIAUoCFEEIIA0gBFkIIIQzwv2Wi9/0HmqC9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x396 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xfit = np.linspace(-1, 3.5)\n",
    "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\n",
    "\n",
    "for m, b in [(1, 0.65), (0.5, 1.6), (-0.2, 2.9)]:\n",
    "    plt.plot(xfit, m * xfit + b, '-k')\n",
    "\n",
    "plt.xlim(-1, 3.5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These are three *very* different separaters which perfectly discriminate between these samples. Depending on which you choose, a new data point will be classified almost entirely differently!\n",
    "\n",
    "How can we improve on this?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Support Vector Machines: Maximizing the *Margin*\n",
    "\n",
    "Support vector machines are one way to address this.\n",
    "What support vector machined do is to not only draw a line, but consider a *region* about the line of some given width.  Here's an example of what it might look like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeAAAAFJCAYAAABDx/6zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\noDRd9j3qI1YAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 576x396 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xfit = np.linspace(-1, 3.5)\n",
    "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\n",
    "\n",
    "for m, b, d in [(1, 0.65, 0.33), (0.5, 1.6, 0.55), (-0.2, 2.9, 0.2)]:\n",
    "    yfit = m * xfit + b\n",
    "    plt.plot(xfit, yfit, '-k')\n",
    "    plt.fill_between(xfit, yfit - d, yfit + d, edgecolor='none', color='#AAAAAA', alpha=0.4)\n",
    "\n",
    "plt.xlim(-1, 3.5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice here that if we want to maximize this width, the middle fit is clearly the best.\n",
    "This is the intuition of **support vector machines**, which optimize a linear discriminant model in conjunction with a **margin** representing the perpendicular distance between the datasets."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Fitting a Support Vector Machine\n",
    "\n",
    "Now we'll fit a Support Vector Machine Classifier to these points. While the mathematical details of the likelihood model are interesting, we'll let you read about those elsewhere. Instead, we'll just treat the scikit-learn algorithm as a black box which accomplishes the above task."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0,\n",
       "  decision_function_shape='ovr', degree=3, gamma='auto', kernel='linear',\n",
       "  max_iter=-1, probability=False, random_state=None, shrinking=True,\n",
       "  tol=0.001, verbose=False)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.svm import SVC  # \"Support Vector Classifier\"\n",
    "clf = SVC(kernel='linear')\n",
    "clf.fit(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To better visualize what's happening here, let's create a quick convenience function that will plot SVM decision boundaries for us:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_svc_decision_function(clf, ax=None):\n",
    "    \"\"\"Plot the decision function for a 2D SVC\"\"\"\n",
    "    if ax is None:\n",
    "        ax = plt.gca()\n",
    "    x = np.linspace(plt.xlim()[0], plt.xlim()[1], 30)\n",
    "    y = np.linspace(plt.ylim()[0], plt.ylim()[1], 30)\n",
    "    Y, X = np.meshgrid(y, x)\n",
    "    P = np.zeros_like(X)\n",
    "    for i, xi in enumerate(x):\n",
    "        for j, yj in enumerate(y):\n",
    "            P[i, j] = clf.decision_function([[xi, yj]])\n",
    "    # plot the margins\n",
    "    ax.contour(X, Y, P, colors='k',\n",
    "               levels=[-1, 0, 1], alpha=0.5,\n",
    "               linestyles=['--', '-', '--'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAdkAAAFJCAYAAADXIVdBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x396 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\n",
    "plot_svc_decision_function(clf);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that the dashed lines touch a couple of the points: these points are the pivotal pieces of this fit, and are known as the *support vectors* (giving the algorithm its name).\n",
    "In scikit-learn, these are stored in the ``support_vectors_`` attribute of the classifier:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAdkAAAFJCAYAAADXIVdBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x396 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\n",
    "plot_svc_decision_function(clf)\n",
    "plt.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1],\n",
    "            s=200, facecolors='none');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use IPython's ``interact`` functionality to explore how the distribution of points affects the support vectors and the discriminative fit.\n",
    "(This is only available in IPython 2.0+, and will not work in a static view)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "eb702b3fab7e48d39ddbc5ec41ca2ff0",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "A Jupyter Widget"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from ipywidgets import interact\n",
    "\n",
    "def plot_svm(N=10):\n",
    "    X, y = make_blobs(n_samples=200, centers=2,\n",
    "                      random_state=0, cluster_std=0.60)\n",
    "    X = X[:N]\n",
    "    y = y[:N]\n",
    "    clf = SVC(kernel='linear')\n",
    "    clf.fit(X, y)\n",
    "    plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\n",
    "    plt.xlim(-1, 4)\n",
    "    plt.ylim(-1, 6)\n",
    "    plot_svc_decision_function(clf, plt.gca())\n",
    "    plt.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1],\n",
    "                s=200, facecolors='none')\n",
    "    \n",
    "interact(plot_svm, N=[10, 200], kernel='linear');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice the unique thing about SVM is that only the support vectors matter: that is, if you moved any of the other points without letting them cross the decision boundaries, they would have no effect on the classification results!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Going further: Kernel Methods\n",
    "\n",
    "Where SVM gets incredibly exciting is when it is used in conjunction with *kernels*.\n",
    "To motivate the need for kernels, let's look at some data which is not linearly separable:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAecAAAFJCAYAAAChG+XKAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBo\ndHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAIABJREFUeJzs3XecVfWZ+PHP6bdOAQakCChKUURF\nCTZQRFSaSIcZhsQYs8mabjabzS9xs5tsko3pdZNoVEB6RwUpgoAoCoIIAiKKXaRMu/203x8Dg+Pc\nOwzDzG3zfb9eecW5595znzncuc/5tucrua7rIgiCIAhC1pAzHYAgCIIgCPWJ5CwIgiAIWUYkZ0EQ\nBEHIMiI5C4IgCEKWEclZEARBELKMSM6CIAiCkGXUTAdw2rFjNZkOoVUUF/uoqIhkOoy8J65z+ohr\nnT4tca2rqip5+OG/ATBq1Fj69busJULLO5n4XJeUBFMeEy3nVqaqSqZDaBPEdU4fca3TpyWudWFh\nEZMmTUVVVVatWs5LL21HlLdoKNs+1yI5C4Ig5LkePXoyfXo5wWABmzZt4Nln1+E4TqbDEhohkrMg\nCEIb0LFjR8rKyunQoYSdO3ewatVyTNPMdFhCCiI5C4IgtBEFBYWUlpbTvXsPDh48wKJF84lGo5kO\nS0hCJGdBEIQ2xOPxMGnSVPr1u4z333+PuXNnUVVVmemwhM8QyVkQBKGNUVWVMWPGMWjQYE6cOMGc\nObM4evTjTIclfIpIzoIgCG2QJEkMGzac4cNHEImEmTdvDm+9dTjTYQmniOQsCILQhl1zzSDuums8\njuOwdOkiXnttT6ZDEhDJWRAEoc3r06cvU6ZMR9cNVq9+khdeeF6shc4wkZwFQRAEunW7kNLScgoL\nC9my5TnWrl0j1kJnkEjOgtBE6vMKwa94KBrtpeDzHvTl2VVRSBDOV4cOHSgrm0mnThfw6qu7WLZs\nMYlEItNhtUkiOQtCE+hPKRR8yYNnqYb2soqxWqPgG168f9YyHZogtKhAIMi0aWX07HkRhw+/yYIF\ncwmHw5kOq80RyVkQzsYF7990lBP1/1ykmITnMQ3EHhBCnjEMg4kTp9C//wA++uhD5s6dRUXFyUyH\n1aaI5CwIZyFVgPp68j8V9R0FbWP+d29Lx8D//3QKR3vhZvD9TIcmFJZSt8gEvmMQvM+D71c6Un5u\nPpeXFEVh5MjR3HDDTVRUVDBnziw+/PCDTIfVZmTNlpGCkK1cHVwjxTHFxS3O71mtUgUUlnrRXj3z\ndeHfbKDuUqieF035LeL9nYbvtwZyVKp7TF+tUjU7itslv69ZvpAkiZtuGkowGGTt2jUsWDCXsWPv\n5pJLLs10aHlPtJwF4WwCYA62kx6yrrKxrs/vGa3ev+r1EvNpxnMqxvzkY+7SUQnv3/V6iRlAe03B\n/5DeKnEKrefKK69mwoRJACxbtpjdu1/JcET5TyRnQWiC8I/jmFdZ9R6zLrYJ/SgBUooX5Ql1b+qv\nCW1H8mOehSrK8RRDAa/k/zBAPurV61KmTSvD6/Wxdu0atmx5TqyFbkVZk5yrq6syHYIgpOR0d6l8\nMkrNL2NEvhwn9MM4lesjWDckb1HnE9fTyEFPM76cxfd5zurcuQtlZeUUFxfzwgvP8/TTT2Lb+f83\nkAlZk5wffvhvvPjiNnEnJmQvHWJfMAn/NEH0GwncQKYDSo/EcAtXavh36fhcYhOsJK+A2GQLu0Py\n7n7rGvFlnsuKi9tRWjqTLl26sm/fayxZspB4PJ7psPJO1iRnn8/H5s2bWLdOVKURGidVgufvGt6/\naUjHMx1N/ouXWkRnmLifaiU7BQ6R+xNYn0v+t+pe4BK9L4HjrZ/UzStswt8VRS1ynd/vZ+rUUi65\n5FKOHHmbefPmEAqJqfgtSfnxj3/840wHAdC9ey/eeecdDh9+E03T6datW6ZDahF+v0EkIr6MWorn\n7xoF/+rFs1JD36hiLNLAAv1WVVzn1iKBeYdN4kYLp52LPlzl5H+GMcc13gK2rncwB9qgudgXOcTH\nWoQeiuGWpCnuPJDN3x+KotCnTz8ikTCHD7/JwYMH6NnzYnw+X6ZDa5ZMXGu/P8UyEEByz6Mf+dVX\nX+VXv/oVs2fPrvf4s88+y5///GdUVWXixIlMmTLlrOc6dqyGeDzOtm1buemmoWhaflReKikJcuyY\nuKNsCeoOmcKpPuSa+jOwHK+LvELi2FXiOqeD+EynTy5ca9d12b79BTZv3oTH42X8+IlceGH3TId1\nzjJxrUtKgimPNbtb+x//+Ac//OEPG4w1mKbJz3/+c/75z38ye/ZsFixYwLFjx5p0TsMwGDZseF1i\nfvPNQ6IqjVDHs0BrkJiB2uU6czMQkCAISJLEddfdwKhRY0kk4ixaNJ+DBw9kOqyc1+zk3L17d/74\nxz82ePzw4cN0796dwsJCdF3nmmuuYceOHed8/qqqSlasWMoTT8zmo48+bG6YQh6RQo2sWapOXxyC\nIDTUv/8VTJw4BVmWWblyGTt2vJTpkHJasyuE3XHHHbz//vsNHg+FQgSDZ5rqfr+fUCh01vMVF/tQ\n1TPrH0tKgkyadDdPPfUUq1YtZvLkyfTu3bu54WZUY10XwjkYACxJcay3uM7pJK51+mT9tXaBlcAb\nUHL9lXT/eifmzJnD9u1bkGWL22+/HUnKjWIA2XStW7x8ZyAQqLeDSTgcrpesU6moaLh7QI8efbj9\ndplVq5bzyCOPM2LEHVx55dUtGm9ry4Uxo1whlUPhIh/a3vpFLMy+Ntp3FHGd00R8ptMn26+1/KZE\n8JsetJ0KkiPhelyKh7Tn7oemsnj1Atav38QHH3zCyJFjUNXsrhadN2POqfTqVTvrurKykkQiwY4d\nO7j66uYn1EsuuZSpU0sxDA/PPLOa117b04LRCrnEDUD141GiUxNYvWysXjbRSQmqH42CmAEsCGkX\n/J4H/WUVyaltGUsxCWOdRtdfdKK0dCbdul3I/v2vs3jxAqLRJuyUItRpsVuZVatWEYlEmDp1Kt//\n/ve59957cV2XiRMn0qlTp/M6d5cuXSkrK2fTpme59NLc7NoWWoZzoUvoj6LgQV5wyfvSp/lM2S2j\nvZy8FKu+VcEreZkyZTpPPbWSgwcPMHfubCZPnkpBQWGaI81N57WUqiWda3fChx9+QPv2HTCM1OvE\nskG2d0vlC3Gd0+e8rnUE/D/R0baqyCGw+jhE7zMxh4uqYclk8+daX6FSeJ836TEn6HLypTBuexfX\nddm4cT07drxMIBBk4sQp591gaw15362dDidOnGDhwnnMn/9EkyabCUKuk46D9w863od0lH052tx0\noeA+D75HDLSDCsoHCsazGsGveVCfS7EZhkvtvtGiaGDWMYdY2J2S/8PYvey6rVQlSeLWW0cwbNhw\nQqEa5s+fw5Ejb6cz1JyUk8m5uLiYfv0u5+jRj3niicc5ceJEpkMShFbjeVSl+BY/gZ8aBB4yKBrr\nx/89I+c2kNCeU9CfaziSppyQ8T3asOiQMU+lcKyXdgP9FN/ow//vBsTSEanQFG47iI03G9Rddz0u\nsVKzQXYZNGgwY8fejWVZLFmykH379qYx2tyTNeU7z6VsmiRJ9Op1CbIsc+jQG+zf/zpdu3bLyrGM\nbC6/l0/y9TrLhyWCX/WinDjzTSclJNQ9Mk6Ji3VV+puUzb3WxkINY0vyaS6uArF7zDPPXaQS+HcP\n6hEFOSohV8houxXUN2Xi45JvtpGNpBpQXpdrd+9K3gPcqGz/XJu32LgaSCFAc7GucIh8O0F8RvJ/\no5KSErp1u5BDhw6yf/8+FEWla9duWbHUKtvKd+ZkyxlqE/QNN9zEyJGjSSTiLFw4j7fffivTYQlC\ni/I8oaFUNPwzlRwJfX1u7Yvsdkjd1HcL6x/zzNWQIw2/sLX1KsruHPjassD/fYPim/y0u8NP8Y1+\nAl8zarvo84kE0W8lqHwmysmdEaqWRYlPa/zmqXv3HkyfXk4wWMDmzRtZv/4ZsdlREjnwKW/cFVdc\nyYQJkykubkdJScdMhyMILUoKp25RNHYsG8VKTaxLG078cnFJ3F7/C105kvx3k6MS+gvZf1Pi/7GO\n7586yke1X7HKcRnvQp3gA9k9gTVdSkpKmDFjJiUlHdm16xVWrFiKaZpnf2EbkvPJGeDii3vx+c9/\nkUCgdoPdysoKsS+0kBfMgTZuisFlq2+OzXD2QM3P45iXnYnbKXSIft4ken/9L2anXfJTuLKL3TPL\nW1lRMNYk777XnlWRjubWTVVrCQYLmD59Bt279+DQoTdYsGAukUjDYlRtVV4kZwBZrv1VTp48waxZ\nj/HkkyuxrNwZmxKEZBKTLBJDGyZh61Kb6Fdyr6VhDbWpXB+h6q9RQv8do2JdhPBD8QbfRJ9tSZ9m\nDrRJ3JHdNyXyMQn5o+RfrcpJGXW/SM6neTweJk+eRr9+l/Phhx8wd+4sKisrMh1WVsib5Hyax+Ol\nffv27N+/j8WLFxCLiemdQg5Taquihb8Sx7zawrzMJjo9QdWjUZweOdo7pEJiokX0KyZOz+S/Q+S7\nCaLlCezi2layq7okBlvU/DqW9d9aTkcXu0uKJUbtHax+Ofrv1koURWHMmLsYPPh6Tp48yZw5s8Rm\nR+RwEZLGmKbJU0+t5I03DtKhQwmTJk3J2EzubC4ikE/EdU6fdF5r+X0J/VkFu6eDOcTJmYpivgd1\n/P/XcHw5NiVBzZ+aXuGurX2uX3llBxs2rENVVcaNG8/FF1+StvfOtiIkObmU6mwURaF3777EYlEO\nH36TgwcP0rPnRfj9/hZ7j6bK9qUQ+UJc5/RJ57V2C8C60qntJciRxAxgDrWRakA+KiFXy9gdHeJ3\nmYQeip9T0eS29rnu3LkLHTt24uDBA7z++j4CgQCdOl2QlvcWS6nSRJZlhg+/nZtvvhXHcdC07N4R\nRRCEPKJA+KcJTm6OcHJzmIptYUK/j4Mn04Flv0sv7V232dGaNU+zdevmNjnBN2+TM9SuhR48+Dru\nvffLFBUVAxCPi00TBEFIkwDYfR3cgkwHklu6du1GWVk5RUVFbNu2lTVrnsa2s3siYEvL6+R8msdT\ne7taU1PNo4/+g+3bX2yTd2KCIAi5ol279pSWzuSCCzrz2muvsnTpIhKJttPF3yaS82mxWBzXheee\ne5Znn10nqtIIgiBksUAgwLRpZVx8cS/efvutNrXZUZtKzqer0nToUMLOnTtYuXKZqEqTq1zQn1QI\nfNMgcL8H/gGIZe2CkHd0XWf8+EkMGHAVH3/8EXPnzmoTmx21qeQMtVVpSkvL6d69B2+8cZBFi+aL\nqjS5xgX/dw0K7vPinafjXaTBl6HgCx5oO71egtBmKIrCHXeM5MYbh1BZWcncubP54IP3Mx1Wq2pz\nyRlqx6AnTZpKv36XcezYJ4TD4UyHJJwDbZ2Cd76GZNdfW2Os1fD+o+HWg4IgZDEX9KUqga8ZBP/V\ng2eWlrQXTJIkbrxxCCNHjiYej7FgwVwOHXoj/fGmSZtdX6SqKmPGjKOi4iTt2rUHwHXdrNi6TGic\nsU5FMpP/O2kvKg3qNAuCkKVcCHzLwLNAQ3Jq/6Y9izX0tQrVj8Ygyb32FVdcid/vZ+XK5SxfvoTb\nbrudq6++Js2Bt7422XI+TZKkusQciUSYPfsx3nrrcIajEs6qsYn2Yo6fIOQMfbWCZ+GZxHyasVbD\n+3DqXrCLL76EadPK8Hp9rFv3DM89tzHvVuC06eT8aZ98cpTjx4+xdOkiXnttT6bDERqRGGbhKsn/\nEM1rRXYWhHocUN6QkN/Lvl5BfYPaYHjqNO0sW4NecEFnZsyYSbt27di+/QWeempVXq2FFsn5lJ49\nL2LKlOnousHq1U+ybdvWvLsTyxeJUTax8WaDrRTjQy2iXxUzwgThNGOxStEdPoqH+ml3o5/CiV7U\nXVmUpBv7im3C129RUTGlpTPp2rUbr7++l0WL5ufNZkciOX9Kt24XUlY2k8LCQrZu3czatWva9Fpo\n6aiE/991iu70UjTai+/HOmTDEkMJQn+KU/PbGLG7TeJjTHgIqp+IivKIgnCK+rxC4AcG2qsKkiMh\nxST0LSrB+71IWbKXRmKYhSun6AUb3LRWsM/nY8qU6Vx6aW/effcd5s2bQ01NdUuGmREiOX9G+/bt\nKSubSadOF7Bv32scP3480yFlhFQFhWUefI8aaK+oaC+r+P9iUDjDmx3LlWSIl1nU/D1G9T9j8F0g\ndQ15QWhzPHM05MqGX/HqmwqeR/QMRNRQYoxNbEKSXrBhFtH7mj6xU9M0xo2bwMCB13Ds2CfMmTOL\nY8eOtXS4adVmZ2s3JhAIMm1aGZ98cpSOHTtmOpyM8P5FR9vT8OOhb1PxzNKIfUnMiBaEbKYcTd19\nLX+YJV3bp3rBzCE2+iYV7NoWc+zzJpzj/cPpzY4CgQI2b97IvHmzufvuiXTv3qNVQm9touWcgmEY\nXHhhdwASiQQrVizl5Mn8r0pzmvp66o+GurvxiRqCIGSefUHqQVuncxbNp5EhPt2i5m8xah6OEbvv\n3BPzaZIkcd111zN69F2YpsmiRfPZv//1lo03TURyboJDh97g4MEDPPHEbD788INMh5MWbmNjt74s\n+sMWBCGp2HQTp6jhnBmrl03sS9kwNtV6Lr+8PxMnTkFVVVatWs5LL23PuQm+Ijk3weWX9+eOO0bW\nVaV5881DmQ6p1cXvSL5cyfG6xO4WXdqCkO2sITah/4ljDrBxJRfXcEncZFHzpxhuMNPRtb6ePS9i\n+vRygsECNm3awMaN63Nqgq9Izk105ZVXM378RACWLVvMrl07MxxR60pMtIjeY+L4zyRop9Ah8vUE\n1g258wEXhLYsPtmicm2Eio0RTm4OU7U0inVN2/n77dixI2Vl5XToUMKOHS+zatXynNnsSCTnc9Cr\n16V1VWk2bFiX32PQEoR/FqdyRZjwt+KEH4hTsSZC9Lv53R0mCHlHBvsyB+ei3OrWbSkFBYV1mx0d\nPHiARYvmE41GMx3WWUlulnTEHzuWJQvvmqCi4iRHjx6lb99+Z31uSUkwp363XCWuc/qIa50+4lq3\nHMuyWL36Sfbvf5327dszadJUCguL6o5n4lqXlKQeXxAt52YoLm5Xl5gty+K55zYSj8czHJUgCIKQ\nyunNjgYNGsyJEyeYM2cWR49+nOmwUhLJ+Tzt3v0K27e/wNy5swmF8vQO1wJ9gYr31zraBqVJZfUE\nQRCyjSRJDBs2nOHDRxCJhJk3bw5vv/1WpsNKSiTn8zRw4LVcffXAU1VpHs+7imLKaxJFd/go/LqX\nwP8aFM70UjDVi5T71fEEQWijrrlmEHfdNR7HcViyZCF7976W6ZAaEMn5PMmyzG233cHQocOorq5m\n7txZvPfeu5kOq2W4EPiBB+21M0VHJFPC2KTi/6GolSkIQu7q06dv3WZHTz+9ii1btmTVWmiRnFvA\n6ao0o0aNJZFIsGjR/LwovK6+KKPtTF4NTH9eATHMLghtjrJHIvhFD+2u8VF8nY/g1wykj7KkHOg5\n6tbtQkpLyyksLGTDhg2sW5c9mx2J2totqH//KwgEApw4cZxgsCDT4Zw35QMZyUr+RydVS0gxcEUD\nWhDaDPmIRMF9XtS3z9y0q28pKG/IVK6IgjeDwTVThw4dKCubyTPPrGT37l2EQiHGjBmHrmd2cxDR\ncm5hPXtexDXXDALAcRx27dqVVV0l5yJxq4XdMfldpNXbwc39+w9BEM6B929avcR8mrZbxfuYloGI\nWkYgEOSee+6hZ8+LePPNQyxYMJdwOJzRmERybkXbt7/AihUrWLVqOZZlZTqcc+a2A3Og3WA7N8fn\n1u4ak5s9WYIgNJPyVuqUoRzK7XRiGAYTJ06hf/8BfPTRh8ydO4uKipMZiye3r2aWu+qqgfTo0YMD\nB/bnTFWaT1NfkdF2KEifycJOgUNiZO7dbAiCcH7cwtTHnGBu9hB+mqIojBw5muuvv5GKigqeeGI2\nH330YUZiEcm5FXm9XsrLy+nbtx/vvfcuc+fOprq6KtNhNZlnloZyPMlm7R8reP6RHZu1C4KQPvFx\nJq7RMAnb7R1i5blRs/psJEliyJCbuf32O4lGI8yf/wSHD6d/syORnFuZqqqMHXs31147iBMnjjNn\nziwikUimw2oS+YNGNmtv5JggCPkpMdom/K1EvbkoVg+b8H/GcS45h5azC55/aBSO91I01EdBuQdt\nbXbtE3/VVQMZP34SAEuXLubVV3el9f3FbO00kCSJW28dQTBYQDQaxefzZTqkJnE6pj7mluR+F5Yg\nCOcu+kCC2BcSGMs0MFxiEy04x6803090fH/VkexTN/kHFLQXFUIPxYjfbbd80M10ySW1mx0tXryQ\nZ55ZTXV1NTfdNBRJav3GiWg5p9GgQYMZOvQWAFzX5f3338tsQGcRm2biFDacrW13t4nm+WbtgiCk\n5raH2JdMYuXnnpilk+BZpJ1JzKfIVTKef+pZVx64c+cuzJgxk+LiYl544XlWr34K2279GwiRnDPk\ndD3uF1/clrVLrawhNqEfxzH71X4QXdUlca1F9W/iuB0yHJwgCDlJX6uiHE2eepSDMlJmVzAlVVzc\njtLSmXTu3IW9e/ewZMnCVt/sSCTnDOnV61IKCgrYvHkT69c/kzVVaT4rXmZRuSFCxYowFasjVD0V\nxRqaPd1OgiDkFqezg6ukaJD4XdwsnWvq9/uZOrWUXr0u4ciRt5k3b06rbnYkknOGlJSUUFY2k5KS\njuza9QrLly/BNLN0tqMK1vUO9pWOWNssCMJ5MYc6mFclv8E3b7QhS5MzgK7rjB8/iSuvvJpPPjnK\nE0/MarXNjkRyzqBgsIDS0nJ69OhZV5UmkRBjuYIg5DEJwj+NY112JkG7iktiiEXov7O/YL8sy9x+\n+50MGXIzVVVVzJ07u1U2OxLJOcMMw2DSpKlcdll/Sko6omm5WwJPEAShKaxrHCrWRqj5VYzwA3Gq\nH41StTiKW5zpyJpGkiSuv/5GRo4cQyIRZ9Gi+Rw8eKBF30MspcoCiqIwevRYXNetm6JfU1OdF5tn\nCIIgJKVDbGaWDuU10RVXDCAQCLBixVJWrlzGsGHDufbaz7XIuUXLOUtIkoQs1/5z7Nz5Mg8//Dfe\neuvNDEclCIIgNOaiiy5m+vQZ+Hx+nn12PRs3bmiRFTgiOWehgoLaArZLly5mz57dGY5GEARBaEyn\nThcwY8ZM2rdvz8svb+fJJ1ec92ZHIjlnoUsv7c3UqaUYhoc1a55m69bNWbsWWhAEQYDCwiJKS2fS\nrduF7N//OosXLzivzY6anZwdx+HBBx9k6tSplJeX884779Q7/tOf/pQJEyZQXl5OeXk5NTWttx4s\nH3Xp0pWysnKKiorYtm0ra9Y8nZaqNIIgCELzeL1eJk+eRp8+fXn33XfOa7OjZifn9evXk0gkWLBg\nAQ888AC/+MUv6h3ft28fDz/8MLNnz2b27NkEg8HmvlWb1a5de0pLZ3LBBZ2Jx2NpqecqCIIgNJ+m\naYwdezfXXHNt3WZHn3zyyTmfp9nJeefOnQwZMgSAq666ir1799YdcxyHd955hwcffJBp06axePHi\n5r5NmxcIBJg2rYzRo++qmzCWtcVKBEEQBGRZ5tZbR3DLLcMJhWqYN28277xz5JzO0eylVKFQiEAg\nUPezoihYloWqqkQiEWbMmME999yDbdvMnDmT/v3707dv35TnKy72oarZtWVYSykpablegz179rBx\n40bKysro0EEUuP60lrzOQuPEtU4fca3Tp6Wv9ejRt9GjxwUsW7aM1auXM27cOAYMGNCk1zY7OQcC\nAcLhMxXKHcdBVWtP5/V6mTlzJl6vF4DrrruOAwcONJqcKypyY4/jc1VSEuTYsZYbb3/nnY94//2P\n+f3v/8KECZPo1u3CFjt3Lmvp6yykJq51+ohrnZpUDd4/66h7ZdAhfqtNfIbZ7BLDrXWtO3XqwahR\n41m+fAmzZ89j6NCPGTz4OiRJavRmoNnd2gMHDmTz5s0A7N69m969e9cdO3LkCKWlpdi2jWmavPLK\nK1x++eXNfSvhU6677gZGjhxNIhFn4cJ5vPHGwUyHJAiCkFbSSSic7MX/WwNjnYbxlEbwuwaBbxuZ\nDi2p7t17MH16OcFgAZs3b2zSZkfNTs4jRoxA13WmTZvGz3/+c/7jP/6DRx99lA0bNtCrVy/Gjh3L\nlClTKC8vZ9y4cVx66aXNfSvhM6644komTJiMLMusWLGUV17ZkemQBEEQ0sb3Ox1tV/2OX8mV8CzR\nULdm5wrhkpISZsw4s9nRihVLG32+5GbJAtp87bppzW6po0c/ZvHihXTo0IHJk6fVTRhri0T3X/qI\na50+4lonV3iXF/3F5KOyka/ECf/3uW8glK5rHYvFWL58Ce+++w4PPfTzlM8TtbVzUQw88zR6nujO\nF674AsrNel1i/nR9bkEQhLzUSOZys3xescfjYfLkaWzYsLbR54nknGPUzQqBHxhob9R+Av16FxLD\nLar/FuPwB4fYuXMHd901Ho/Hk+FIhbYrgsfzGLJ8AtMchGnegdgIXGhJ5uds9K0N05cTcIlPzP6l\npoqicPvtIxt9TtvtB81FJgR+dCYxA0gJCWO1hv+nOvv37+fIkbeZN28ONTXVGQxUaKs07VmKi28k\nGPw+fv9DFBaWUlAwCQif9bWC0FSRbyWID6tfu9r1uES/nMDunxUjtedNJOccYixT0fYn77PRtqiM\nGjWGgQOv4dixT5gzZxbHjh1Lc4RC22bi9/8AVT1c94gkWRjGOvz+BzMYl5B3PFD9RJTq30eJliaI\nfjFB5fwIke+f+1hzthLJOYfIJ1J3Dcqh2qo0w4ffzs0330pNTXWzqtIIQnMZxhI07fWkxzRtS5qj\nEfKeCvHpFqHfxQn9Io51Q+NLk3KNSM45JD7cwilI/gG0+tQ+LkkSgwdfx5gx4zBNk+ef3yJ2tBLS\nQpaPN3JMdGsLwrkQE8JyiNPbJT7WwvOEhvSpCTZ2e4fol+pPgrjssssJBoMUF7cTs7eFtIjHx+Dz\nPYQsVzQ4ZlmXZSAiQchdIjnnmNCv49jdXfT1ClK1hNPLIXKPiXVzw+0kL7ywe91/v//+exw69AY3\n3zys4XpoGzwPa+hbFIiB1d+6kr8FAAAgAElEQVQh+vUEbvvW/m2EfOI4PYnFJuL1PoIknemtse2O\nRKNfyWBkgpB7RHLONTJEv50g+u2mv8R1XbZseY733nuX6uoqRo0ai6Zppw5C8H4Dz1K97vnGZtCf\nV6iaF8UVe2sI5yAc/jW23RPDeAZJqsS2exGNfhnLuinToQlCThFjzm2AJEmMHz+J7t17cPDgARYt\nmk8kUrvRiLZewVilNXiN9qqK7w96g8cFoXESsdg3qKp6isrK56mpmSUSs3D+HKCNTZ0RybmN8Hg8\nTJo0lX79LuP9999j3rzZVFVVoj+nIJnJx6TVPVleakcQhLymP61QMMlDu6v8FN/kw/99HaKZjio9\nRHJuQ1RVZcyYcQwaNJgTJ06wevVTuA0bzXVcrY3dqgqCkDW0tQrBb3kwNmsoH8uohxR8/zQo+HLb\nqH4oxpzbGEmSGDZsOO3ataNnz4uI9zfxPq4jhxq2ns0b82vdoCAIucP7uIZc2bD9qG9SUZ+XsfL8\n+0m0nNuoK6+8msLCIuz+Lm/PfJddnt11x1zZJT7SJHp//lTbEQQhtyhvJ09PUlxC257/7cr8/w2F\nRrmuy+LuSzg56TifVB1jSLuhmDfZJMba4tZNEISMcYtSD6s5nfO71Qzi67fNkySJceMmEOxTwPo+\nz7L0thXExprikyEIQkbFR9i4SaZom5fZxCdZSV6RX8RXsED79u0pK5tJp04X8Oqru1i2bDGJhOjS\nFgQhc6LfTBD9vIldXNtKdiUX80qL0C9j0MhE1nwhkrMAQCAQZNq0Mnr2vIjDh99k9eonMx2SIAht\nmQzhh+JUro1Q8z8xqh+JUrkmivW5/O/SBjHmLHyKYRhMnDiFjRvXc+WVAzMdjiAIAk4Pl9h95tmf\n2BosMBaoqAdknBKI3ZPADabnrUVyFupRFIXbbruj7ueKipNEo1G6dOmawagEQRDSS/pYouCLHvQd\nZ9KkZ45K6KE4ZpK9DFqa6NYWUrJtm6VLF7FgwVzefPNQpsMRBEFIm8B/GvUSM4B6RMH/E6O2nGgr\nE8lZSElRFG655VYAli1bzO7dr2Q4IkEQhDRIgPZS8vSoviajrW/90sYiOQuN6tXrUqZNK8Pr9bF2\n7Ro2b96E64qynoIg5DETiCXfc0ByJeSTyY+1JJGchbPq3LkLZWXlFBcX8+KL29i4cX2mQxIEQWg9\nfrAuTz6ubHe1SYxu/XXWIjkLTVJc3I7S0pl0796Dvn0vy3Q4giAIrSr6FRO7pP7gsmu4RMustMzY\nFrO1My0Onrka8scS1gCbxCgbWr/HpFn8fj9Tp5YiSbUBhkI1QO0aaUEQhHxi3mZT/UgUz+M66jsS\nTnuX+F0W8cnpqU4mknMGqS/JBL7rQTtQO7nAlV3MG2o/EG5xhoNL4XRiNk2TxYsXEotFmTRpGh06\ndMhwZIIgCC3Lus4hdF0sI+8turUzxYXAg0ZdYgaQHAl9q4r/QSODgTWNqqr07duP6upq5s6dxXvv\nvZvpkARBEPKGSM4Zom2UUXcnn46vb1NqZwtmMUmSuO66Gxg1aiyJRIJFi+Zz8OCBTIeV8yTpJKq6\nHUk6melQBEHIIJGcM0T+WEZyUgwuhyWIpzee5urf/womTpyCoiisXLmMXbt2ZjqkHBUnELif4uLB\nFBePoLh4MIHA/eTMB6EeF11fSiDwLwSDX8LjeYSsv9sUhCwjxpwzJHGnhd3RQfmk4f2R3deBQAaC\naqaLLrqYadNmsGzZIoqKsnSwPMsFAg/g9c6u+1lRjp76WSEU+kOGorLxev+Mpm1EkuJYVn8ikW8B\nfRp5jUsg8HU8njlIUu1MV49nIbq+murquYCejsAFIeeJ5JwhbjuITTHx/VVHss+0oJ0ih+gXc2+7\nxk6dOvGlL30FVa39SMViMVRVrftZSE2SKtH1Z5Ie0/U1SFIVrlvYzHMfw+f7OZq2AwDTvJZI5D9w\n3ZKzvNI91epd8qlYtqJpW4E1QEHKeD2euXWJ+TTDWIvX+xei0W816/cQhLZGfHNmUORHCZyuLvpq\nBfm4jNPTIVpuYg5v/aLqreF0IrYsi2XLFgNw990T8Xq9mQwr68nyERTlaNJjivIxsvwutn1FM84c\norBwMpp2puyqpu1G016hsvJJGuue0bT1GMbKJI/vBf4X+J+kr9P1Z5Ck5EtNNO0FkZwFoYlEcs4k\nCWL3msTuzb/xOJ/Px8GDB5g7dzaTJ0+loKB5Lb+2wHEuwrY7oygfNThm211wnB7NOq/X+5d6ifk0\nTXsFr/evRKP/lvK1ur4RSUr1uVxDQcHryPLHOE5XYrFSEokJp441Vtr13Mq+SlI1Xu+v0bSduK6M\nZQ0mEvkOIG72hPwnJoQJLU5VVe66azzXXjuIEyeOM2fOLI4eTd4yFMB1C4nHRyU9Fo+PwnWTdyGf\njarua+TY3rPE1NjY8CEMYwOatg/DWEsweD8ezz8BSCRG4LrJVyHI8odoWvLu+4bCFBRMxO//Lbq+\nGcPYhN//vxQUTENMLhPaApGchVYhSRK33jqCYcOGEwrVMH/+HI4ceTvTYWWtcPiXRCJfwra74bpg\n292IRL5EOPy/zT6n6/qbdQwgFivFcZrW2yHL4VPJ2SaRGE0sNplke6No2h4KC8vxes/+O3m9f0bX\ntzd43DA24vE83qS4BCGXieQstKpBgwZz113jsW2bWCwzlXZyg0Y4/BtOnnyJioqdnDz5EuHwbwCt\n2WeMxyfgug0L2riuQTw+IckrznCc3kQiD+C6TRv5UtXXkeX3AIlQ6P+oqfkVtt0wuUtSDK/370jS\nx42eT9NebeS9XmpSTIKQy0RyFlpd3779+PKXv0rfvv0AsG1bbDuZUgDbvpSWWEtnmrcRDn8bxymq\ne8xxigmHv41p3nbW10ej9+M4TVsa5zhB3FO7ASjKHny+v6EoVUmfqyjH8HgWNHq+xrvVs7+CniCc\nLzEhTEiL05tjOI7D8uVLKCgoYPjw25FlcX/YmqLRHxCPT8cwapNhPD4Nx+l5DmdoWsvdtvvhuu0B\n8Pt/hqoeOssrGt+sPh4fgWEsRZLq38S5rk48Pq5JMQlCLhPJWUirWCxGdXU1hw+/SSgUYsyYcWha\n87tuhbNznIuIRr/fjFdqmOYgFGXFWZ+pKAfRtI1Y1sCzdjvb9gXEYqWNPieRmE4s9gIezzwkqXbd\nv+P4iMW+2KRWvyDkOtFsEdLK5/MxffoMevToyaFDb7BgwVwikUimwxJSiEZnYttnK1gCinICr/f/\nAAdJSr1O33VVTPMGdH0lhYWjKS4eQGHhbXg8f6D+UiuJUOiPVFYuJRK5n0jk61RVrSIc/tl5/06C\nkAskN0sG/44dq8l0CK2ipCSYt7/b+bBtm9Wrn+L11/fSrl07Jk2ael6lP8V1bmkOfv938HiWIMvJ\nx44/y7Z7cPLkaxQUjMMwNjb6XNeV6nVZu65MJPItIpEfn0/QeUd8rtMnE9e6pCSY8phoOQsZoSgK\no0ePZfDg6zl58qTYcjIFVX0Jw3gMWU7vMjSv93d4vf9scmIGcJzaSWyRyAPYdrdGn/vZsWRJcvB4\nFiFJ1ecerCDkITHmLGSMJEncfPMwevfuQ+fOXTIdTlaRpPcoKLgfTXsBSYrjOEXE43cSCv2JdGwe\nUVvT+9xeY5pDAbCsoVRWLsfr/RuquhdNe7FBMk5GUd7D5/t/xOMzsaxBzQlbEPKGaDkLGXc6Mbuu\ny+rVT7Fnz+4MR5R5BQVfQ9c3IUm1W0bKciVe73z8/h+m5f0lqbLJz3VdjXj8DsLhH9c95ji9CYd/\nTSTyvSYl5trzgM/3OEVFYygomAqEzjFqQcgfouUsZI3q6irefPMQr732KjU1Ndxww01I59p8ywOK\nsgNN25b0mK6vJxy2aN6fro2mPYUsnySRGIfrph7jd5xLgQMNHnddkKQCLKsE2+6MZQ3GNG/CNG8F\nGv5bmeaNWFYvVPXwWaM7/U8tSVEMYzWBwL8RCv21qb+cIOQVkZyFrFFYWERZWTmLFy/g+ee3UF1d\nze2334miNL4mNt+o6oG6FvNnyfJxJCnchC0kzVNbTRYBKpq2Ab//R6jqXiQJbPsXRKMziUb/DY9n\nDqq6E9f1Eo9Pw7KuIRq9F1V9AUU5Xu+sicSdGMZCKips6q9VjuH1/glN2w5ImOZ1RKP3Ax6i0XsI\nBH6KJJ2pEPfZCWHJ6PomIIrY6EJoi0RyFrJKu3btKS2dydKli3jttVcJhWoYN24Cut7646zZwjSH\n4DjFyHJFg2O23fMsG2FY+HwPYhirkeVPsO1uxON34vEsRVXfqXuWonyI3/8bDGMpmvZG3eMezxNE\nIt8lFvsCpnktsA1ZjuI4ARKJMYRCvzo1w/TTs1oTFBRMwzCerXvEMNagac9TXT2fWOwbOE5nPJ5F\nyPInOM4FqOo2FKXxrnNJqkSSqnFdkZyFtkeMOQtZJxAIMG1aGRdf3Iu3336LAwdez3RIaeU4PZLu\nUuW6OrHYNJJ1H58WCDyA3/8nVPUwslyDpu3H7/9tvcR8miQl6iVmAFkO4fX+jsLCu/B41qAo1UiS\niaJUoKqv1RUE+TSP5+F6ifk0w1hXt0lFIjGZ6uqFVFZuIhz+0VkTM4Bt98J1z77GWmh7pCoI/JtB\n0RAfxZ/zEfyiB/WV/BoCEy1nISvpus748ZM4cGA/l112eabDSbtQ6A84TjGG8QySdALH6UksNpVY\n7KspXmGi6yvQ9aUNjpzrsL2iVCZNnpq2G6/3L8DPPvN4w92jzhzbRiz2pXqPOc6F2HYXFOXDlK9z\nXYNYrAzRfhAasKHg8170bWfSl3pEQdsjUzk7itMvK0p3nLe8Ts7qizKex3TUIxJOO5f4WIv4dCvT\nYQlNpCgKl1/ev+7nrVs3c9FFF9O1a+NraPODRiTyMyKRn1A77uonVYvZMJ7A6/09mtZwAldLU9Ud\nyR5N+XzXbVia1XULiMdH4vM90uCY4/iwrAHEYtOIx794PqEKecpYqKJtazgPRXlXwfd3ndBvk8/X\nyDV5m5y19QrBb3pQjp2589Y3qyjvJoj8e8OuOSG7HTt2jBdf3MZLL73ImDHj6N27T6ZDShOFxnao\nUtXtBAL/gSw33k3sODqy3LTPveOoyHLym9jautkfAGfGvWs3qVicZJMKmUTi9qTnCYd/CYBhrEZR\nPsS2uxCP33lq/+rGdp0y8XhmoaovAhqJxEgSiTE01tUv5Bd1r4yU4t9bOZw/PS3585t8hvdvWr3E\nDCAlJDxzNc5hCaeQJUpKSpgwYTKyLLNixVJeeSVZC67t8XhmnzUxA8Tj40kkhiRtyX6a68rE4yNS\nPq92G8hf1nsskZhKLFZab+9n11WJxWaQSKTaN1ojHP4tFRUvcfLki1RUvEQ4/DsaT8xxCgqmEQx+\nG693AV7vHAoKPo/f/0Cjv5OQX9zUFS9xg/nRpQ3nkZwdx+HBBx9k6tSplJeX88479SecLFy4kAkT\nJjBlyhQ2bmy8zm6Li4G6L/nyG+UjGf3JvO0wyGsXX9yLadPK8Pn8rF+/luee29jm94WW5eONHrft\nYmKxKUhS9FS1MTPlc02zFzU1fyIUmo9pXtXIWXd95meJUOgvVFc/QTR6L9HovVRVzScU+iNna9G6\nbgG2fdlZZqDX8nr/iGGsq//OkoXX+zhe7w8JBL5KIPANNG1dijMI+SD6BRO7k9PgcVdxiY/Mn2HL\nZifn9evXk0gkWLBgAQ888AC/+MUv6o4dO3aM2bNnM3/+fB555BF+85vfkEiksStZBTzJv7RdXJx2\nbfsLPZddcEFnysrKadeuHdu3v8Drr+/LdEgZ1VgN61hsDJWVW7Csfng8K5Gkxr+4XDdIPD4dWT6C\naV7TyDOTLW2SSCRGEgr9llDot5jm7bR0V7OmvZD0cUky8fv/gNf7BF7vYxQWTsfv/16LvreQPdwL\nXML/FcPqeWb3M7vYIfLlBPGy/EnOzW5C7ty5kyFDhgBw1VVXsXfv3rpje/bs4eqrr0bXdXRdp3v3\n7hw4cIABAwacf8RNoByQcFP8ZlZ/B/OO1FvaCdmvqKiY0tKZ7N79Sl7M5Na0p/B6H0NR3sJ1i4nH\nRxKNfpum3DtHo/+CYTyNorxf73HLuoRQ6A+4bgc0bXOT4lDVQxQV3YCqvoHr+nFdNUVCv7VJ52t5\nqW+qPz0jXZISeL2PEo+PwbKGpiEuId3iE2zid0bwLNKQQhC/y8K5ML8aXc1OzqFQiEDgzEQVRVGw\nLAtVVQmFQgSDZwYG/H4/oVDjdXKLi32oagtUgtoGfAFItsnRxaD9RqHkgkYGLVpBY9uCCc0VpEeP\nkXU/vfLKK1xyySUUFJy9ezS7LAa+CpwZN9a0lwgEjgF/bsLrBwKzqF3etIPahH4dqvrfdOhw0ann\nNK01IcthZHk/wKd2h1KA0zezKjAeeICSkkwMDV0NrG/SMyUpTnHxM8DoVo0oHcT3RyO+W/t/qadM\nnptsutbN/gsLBAKEw+G6nx3HQVXVpMfC4XC9ZJ1MRUWkuaHUU/ATD8a7DSezOD6XinlhnItcONYi\nb9UkYj/W1vfhhx+wcuVKZNlg0qSplJTkTuGKgoI/YRgNJ3TZ9gIqK+/HcS486zlkuR2GMQi4nERi\nIrZ9ery49nPn9/fF59vSrPhc1yGRGIwk2VjW5YTDP6OkRM3IZ9rrhcA5fAtHo1FCodz+2xPfH+mT\nN/s5Dxw4kM2ba7vLdu/eTe/eveuODRgwgJ07dxKPx6mpqeHw4cP1jrcat3aafTJyREJfJyaC5aPO\nnbtw2223UVNTzbx5s3n33YbVsLKThaomX5usKCfQ9TVnPYPP91OKi28hEPg5gcDvKSq6C5/vp/We\nE4l8B9NsXve/JLno+svo+g58vscpLr4JWNmsc50vWQ6f/UmnuK5KIjGiFaMRhNbV7Gw1YsQInn/+\neaZNm4bruvzsZz/j0UcfpXv37gwfPpzy8nJKS0txXZdvf/vbGEZjSyRaiARuI2+TT9PshTMkSeKm\nm27CshTWrHmKRYvmM2rUWPr1uyzToZ2FgusGgaMNjriuhG03vse1pq3F5/t9vU0yZLkSn+/3mOZg\nTHPEqXN1papqET7f71DV13BdDVk+iaK8jyxX4jgBXNdAUU4kfR9JOjMzVlXfBh4AtgK+c/2Fz4tp\nXt2kDTNcF2KxiSQSd6YpMkFoeZKbJWtRWqo7IfAtA+/chpskWL1sKjZFGl9G2QpEt1R6nL7O77xz\nhOXLlxCPx5k0aQoXX3xJpkNrlN//HXy+hxs8bpoDqax8lsY6twKBr+L1PpH0WDQ6g1DoL42+tywf\nQVV3YFkD0LTtBIPfSbkb1mfV1PyaWOy+Jj235dgUFo5D1+tPcKstYDIKRfkQ19UwzVuJxT5PPpRx\nEN8f6VNSEuTYxzXoq1SUjyXiwyycPq2bHhvr1s67ft7wj+Ioh2X07Wd+NbuzQ/g/4mlPzEL69ejR\nk+nTy9mx4yV69Ljo7C/IsHD4pyjKB+j6hrpNJSyrP6HQLzlbcpGk1PM0JOnsXcCO05NEoicA8fgl\np3aoeh5ZjuG68qkWdvJkLdVV8nHR9ZVo2nZcN0A0eg+u2/ms7908CtXVT+D3/yequg1JimFZA4hG\nv4ZlXddK7ym0GS9A0Vd8qHtqK5D5gi7xUSah38Xr746aJnmXnN32ULUsijFfQ90v4RZA9B4Tt2NW\ndBAIadCxY0dGjRpT9/Nbbx3mwgu7o2mNV8fKDB/V1QtQ1c1o2nYcpzPx+FTg7LHa9uXAsqTHLOuK\nc4oiEPjGqRuE2p8/3ZXdkP/UeG6UgoJydH193fM9nkcJh/+LeLz0nN6/qVy3kFDod61ybqENs4B/\nBW3PmSws10h4F+g4XV0i309/yee8S84AqBCfYZIf5c+F8/Huu++wZMlCunbtxvjxk/B6s3NvYMsa\nes5rciORf0XXV6NpO+s9bprXEI1+pcnnUZTteDxzG+xeJUlxHMdI0nqegG1fhc/3Qwxj7WfOdRS/\n/wckEnfiuu3qHpfl91GU/VjWAFy3U5NjE4R00JeqsDvFsWfVjCTn3B+UEYRGdOnSlb59+/H+++8x\nd+4sqqrSUVjdwTDmEAzeSzD4RTyeR2jqWuNzE6CqaiGRyH2Y5tWY5tVEIvdRVbWQc1n5WTvWnDw+\n1y0mFpuAaV5OInEdodD/Ax4FQNe3Jn2NopykoGAytUVDwgSD91BcfCNFRRMpLr6eQOArIG6dhSyi\nfJw6FWZqL4b8bDkLwimqqjJmzDgCgSAvv7ydOXNmMWnSFDp1uqCV3tEhGLwXw1hS1xL1eBaj6+uo\nrp5DS//JuW4J4fCvm/16STqJLL+d8rjjFFJT81i9xwKB011/qROspu1A19dgGEvweJbUPa4ox/F6\n5wI6odAfmh23ILQkc4gFPgOSTOOwezU2xNN6RMtZyHuSJDFs2HBuvfU2IpEw8+bN4aOPPmyV99L1\nhfUS82mG8fSpFnR2keXjyHLq6n2W1R9V3Uow+AWKioZSUHA38H+Ai2WlXjtduz56KZqWvKKXri9H\nksQsZCE7WFc7SYvJOUUO0c+n3iymNYmWs9BmXHvt5wgGC9i1aycdOrROFTFd39QgMZ+mac8Ti/1L\nq7xvc9l2DxwniKI0TJSuC6Z5FQUFn0dRPl1W7zl8voNEo9/EMJ5ElpPPGpekChTlZNJjslyJoryE\nZQ1viV9DEM7fbAh3iKNvUpGrwbrEIXaPiXlnZvZiEMlZaFP69OlL7959kE5l0OPHj9O+ffu6n9se\n49T/GiZnSQKf75HPJGYAG49nHtHo14lGP4/f/9cGr3VdiXh8LLr+XNLlWJIEhrFWJGchexgQ+a8E\nEdI/+SsZ0a0ttDmnE/F7773L448/wrp1a3CclhlXSiSG4brJE71pDmmR92hpjpN628lU+0UrylEM\nYyWRyH8Rj9/c4Hg8PoFEohzH6ZDy3E1Ziy0IbZVoOQttVnFxMR06lLB79y5qamoYO/ZudL1hdblz\nkUhMJh5/BsNYXK97Ox4fTSx2z3lG3DpM8wY0reE6EtvuTO1664Zj0q7LqcTrobp6EV7v/6FpL+O6\nMqZ5C7HYFwCZRGIEqvpY0ve1rL4t+FsIWcEF/WkFfZMKCsRGWVhDxRa9zZF35TuzjSi/lx7Nvc7x\neJwVK5Zy5MjbdO7chQkTJuP3+88zGgfDmIembUKSHEzzJmKxcrL3XjhMQcH0euPltt2BcPhBNO0l\nvN45DV5hmgOorHyOVKWTJOl9AoEfoGlbkOWTDephm+bVVFauAbJz3Xm2yKnvDwcCXzPwLNOQ7NoP\nkqu7RMtNwj+LQ5aPHGXbrlQiObeynPrjymHnc51t2+aZZ1azd+8eiouLmTx5GkVFxS0cYbaz0fXF\np1q/AWKxL+A4PZGkkxQUlKNpWz+VYC+louLXWNYtKc5lUVh4B7r+cr1HXVfGcTqRSNxCOPwgrtu1\nNX+hvJBL3x+eWRqB7xpIn8nCruZS9VgUc0R2t6CzLTln6628IKSNoiiMHDmaYDDIG28cxDA8mQ4p\nAxQSiakkElPrPeq67aiqWoWuL0NV9+C6HQgEvollpR6jN4y5DRIzcKoXYTCh0N9aPHoh87TnlAaJ\nGUAyJYzVatYn52wjkrMgUDtJbMiQmxk8+Pq6cedoNNpC5T5dVHU7svwhpjkM1821VrlMIjGRRGIi\nAIGAn9rZ3RaGsQBZfg/LugrTvAOQUNU3Up5JUd5LccRF09ahaVsAH9HoF1pxAw2hNaQoMlerNQrk\n5TmRnAXhU04n5qNHP2bBgrkMHXoLV101sNnnU5TXCAT+DU17GUkyse3OxGJTiUT+i6wfhGuEorxK\nMPg1NO1VAFxXwTSHUF39GI6Tuvqa4yRbX56goOAedH0NklRb8MHjeYRw+EHi8ZmtEb7QCsyrHYzV\nDR93cTGvF63mcyWWUglCEo7jIEkya9euYcuW52je1AyLYPBr6Pq2uqSjKB/h8/0Bj6fxvZazm0sg\n8L26xAwgSTa6volA4PtEo1/Esno3fJVrEI9PbPC4z/cQhrGq7hoBKMon+P0/QZI+u8ZayFbRf0mQ\nuKFhEzlxh0V8img6nyuRnAUhic6duzBjxkyKi4t54YXnefrpJ7Htc7v71/XFqOquBo9LkoNhrGqp\nUDNgG5q2I+mR2m5pmZqaP5FIfA7Xre2cs6yehMPfP7Ud5mdf81zScynKUTyex1oqaKG1eaFqbpTw\nd+PEbzWJjzAJ/ShG9T9jGdkPOdeJbm1BSKG4uB2lpTNZunQR+/a9RjgcYty4CRiG0aTXK8p7KUt5\nynIutwjfr9fK/TRJqkGSIljWdVRVrUNVX0SSTmCatwK+FK+JpnwnSUpeGlTIUj6IfC87KmzlOtFy\nFoRG+P1+pk4t5ZJLLqWi4iSm2fQi+JZ1ZV3L8bNsu0dLhZgBt2PbXZIesay+n5rwJmFZ12OaY0iV\nmGtfc0XSx13XQyIx4jxjFYTcJJKzIJyFruvcffdESkvLCQRq90luSrlP0xxBItGwZKfjBE4VJWkZ\nsvxxmsdmi4nFpuG69fsqHSdILHYv5zrRLRL5BpbVq8Hj8fhYLOuG8wlUEHKW6NYWhCaQZZlgsACA\nkydPsHTpIu68czTdul3YyKskamoew3X/HU3bgiTVYNt9iEa/SCIx/rxj0rQN+Hy/OjWurWCag4hE\n/h+WNei8z302kch/4jidMIyVyPJxbLs7sdhMEolx53wux+lLVdV8fL4/oar7cBw/pjmMaPSbrRC5\n0FrU52X0zSpuwCVWbuIWZTqi3CYqhLWyXKrwk8vSeZ0PHjzAqlXLkWWZ0aPvok+fptSIjiFJYVy3\nHS2xhEqW91NYeDeq+lG9xy3rYior1+O6qTecOF/iM50+OXGtTQh+1YOxRkVK1H627a424R/FiU/I\nnSVU2VYhTHRrC8I56tOnLxMnTkGWZVauXMaOHS814VUeXLc9LbW22ef7R4PEDKCqb+H15vIyLSHX\n+H6j41mp1SVmAOUDBaIOTCwAACAASURBVP9PDKTqDAaW40RyFoRmuOiii5k+fQY+n59nn13Pxo0b\nmrkWunlk+YNGjr2ftjgEQduSfJ2U8oGCZ7aW5mjyh0jOaSRVg/fPGt5f6qg7xKXPdZ06XcCMGTNp\n3749+/btJRxuuLVia0leaev0sY5pi0MQpHDq3iAplLtV8DJNTAhLE2Oxiv9/dJQPau8ynT/rxMeY\nhP4QFwv0c1hhYRGlpTOpqakhEEg9ftTSYrGZ6PqTKMrJeo/bdhdisfvSFocgWH0dtH0Nv8Rcj0vi\nFlEZrLlE8y0NpBPg/4lRl5gB5KiEd5GO9896BiMTWoLX66Vjx9rWak1NNYsWzae6uqpV39OyPkc4\n/L+YZn9ct3Y7RtMcSE3N73CcXF5DLeSa6Ffj2N0bTvyKjzSxBp99yaGQnEjOaeCZraN8lPxS6xtF\nszmf7N+/n7fffos5c2bxySeftOp7xeNTqazcQlXV01RUPENl5bOY5p2t+p6C8Fn2AJeqf0aJTk5g\n9rdJDLYIfy9OzZ/jmQ4tp4lu7TSQGpmd32BMxgV9sYqxTkWKgdXfIfrVBG76ekyF8zBo0OcA2LRp\nA/PmzebuuyfSo0fPVnxHBdO8qRXPLwhnZw9wCYlk3KJEyzkNzBtsXC35TF6rb/3uIP/3DQq+7sGz\nXMNYo+H/lUHBJC/SyaQvF7KMJEl87nODGTv2bizLYvHiBezbtzfTYQmCkGNEck4D81abxG0NJ0bY\n3W2iXzlTJF7dKeOZryE59VvT+i4V32/F2HQu6dfvMiZPnoamaWzYsJZIRGzgIAhC04lu7XSQoPrv\nMXy/dtC3KhCRsPo5RP81jn35mRa1/pSKHE2+9EDdJcamc0337j2YPr2caDSCz5d64wdBEITPEsk5\nXQyI/CBBo+2nxvKv6OPISSUlZ9YjR6NRXnhhK0OG3IKmieIM/7+9e4+vojwXPf6bNTPrmpUAIaCi\n4SaRi9yCrRcEFCkI9QaSkERId8F2Yzdnb7Tbg+2np4duPe7qbs/Z27Z279bLFgSCQSiKF0SMUIVS\nARURUOTmjWsgJCvrPjPnj5RoTAIa1lqz1srz/Yusiczjy6x55n3nfZ/3fCjKSbzeX6LrbwEWsdgo\ngsGfJLVsqRCpJMk5jYSnxfA87sTRxsL92Lczp0ataNtf/rKJrVvf4vDhw0ydOl160x0WJDe3BKfz\nreZPdH07ur6durrngRz7QhMiQaQ/lkbMQRahH0Sx3C0nj0WvjRO8WzYwz3Rjx17H4MGX89lnn7J0\n6SLq6k7ZHVJG8nj+s0ViPkPXt0ldcZE1pOecZoI/iRK9No57tQ5hhXixQXhmDGQ+WMZTVZXvfvdm\n/H4/W7Zs5umnFzF9eikXXHCh3aFlFE1rf/b72Y4JkUmk55yG4mNMAr+KEPhtmPBsSczZRFEUxo27\nngkTJhIKBamuXk40KqMi34Rlec5yTF4ViOwgPWchbFBcfAV+fy6WZeF0ytPXNxGJTMXtfgZFaVn0\nwrJcRKO32hSVEIklPWchbDJgQBFFRZcBEI1Geeed7SnddjJTxWITCAb/CdPMa/7MNHMJBv+BaHSy\njZEJkTjScxYiDbz++nreeedtDh8+zMSJN6Kqsq79bILBnxEOl+NyLQcgEinBNAfYHJUQiSPJWYg0\ncM01Yzhy5AjvvfcugUADt946TYa7z8E0+xMK/dTuMIRIChnWFiIN5OTkUFZ2B/369efAgf1UVS0h\nEAjYHZYQwiaSnIVIE06nk6lTpzN06HCOHDlMVdXTxOOyWb0QnZEMawuRRlRV5cYbp5Cbm4vf70fT\n5CsqRGck33wh0oyiKIwePab553g8zueff0ZhYW8boxJCpJIMawuR5l599RWWL1/K229vszsUIUSK\nSHIWIs2NGDESj8fLunVr2bChRtZCC9EJSHIWIs1dcMGFzJxZSbdu3diyZTMvvPA8hiG7lAmRzSQ5\nC5EBunTpSkVFJb16XcyuXTtZsWI5pmnaHZYQIkkkOQuRIbxeL6Wl5QwYUESfPv1wOOTrK0S2ktna\nQmQQXde57bbbm382TZP6+tN06dLVxqiEEIkmj95CZBhFUVAUBYCamldZtOhJPv74kM1RCSESSZKz\nEBnsggsuIhaLUV1dxe7du+wORwiRIB0a1g6Hw9x7773U1tbi8/l46KGH6NatW4vfmTt3LnV1dei6\njsvl4rHHHktIwCLJouD4VMHqZmF1sTsYcS5DhlyOz+dj9eqVPP/8nwgEGrjiim8396yFEJmpQz3n\nZcuWUVRUxNKlS7ntttt49NFHW/3Oxx9/zLJly1i8eLEk5gzheUSny3gv3a720fVqH/4fulFO2h2V\nOJc+ffpSXj6LnBw/NTXrqal5VdZCC5HhOpSct23bxpgxTeUFx44dy+bNm1scP3HiBPX19cydO5fy\n8nJqamrOP1KRVO7HNXwPudA/VFEsBbXWgftPOv67PHaHJr6GHj16MHNmJd27F+BwqNJzFiLDnXNY\nu7q6mqeeeqrFZ/n5+fj9fgB8Ph8NDQ0tjsdiMWbPnk1lZSWnT5+mvLycYcOGkZ+f3+55unb1omnZ\nucF8QYHf7hDObQ0Qa/2x602Ngvf9cF2qA/rmMqKdk6igwM/8+f+A0+lEURQsyyIajeJyuZJyLpEa\n0tapk05tfc7kXFJSQklJSYvP5s2bR2NjIwCNjY3k5ua2ON69e3fKysrQNI38/HwGDRrEgQMHzpqc\nT50KdiT+tFdQ4Of48YZz/6LNuh30otLGw1EUAhvChIa0kbnTSKa0c2pEAXjzzT+zZ89upk8vJS8v\ncRMIpK1TR9o6dexo67M9DHRoWLu4uJgNGzYAsHHjRkaNGtXi+KZNm5g/fz7QlLz37t1Lv379OnIq\nkSJmz7bfUVq6RXywVKLKNGd6zbW1J3j66UUcPXrE7pCEEN9Ah5JzeXk5e/fupby8nOXLlzNv3jwA\nHn74YXbs2MG4cePo3bs3paWlzJkzh3vuuafVbG6RXsI3x7HU1gk6dqVBbJzUcc40iqJw/fU3MH78\nBILBRpYte5oDB/bbHZYQ4mtSrDSZ1pmtQzcZMyxlgfeXTlwrNbRDKmaORWx0nIaHI1gXpsUlclYZ\n0842+OCDPbzwwnOYpsmkSVMYOnTYef190tapI22dOuk2rC3lO23k2K3gelkHr0W4IoaVyrkIFujr\nVbR9DmJXGsRHmAR/EiX4j1G09x2YF1mYF6d/UhbndtllA/F6vaxa9SyfffbpeSdnITKR/pqKZ5GO\n46ADs5tFdHKc8J0xSNOFDZKc7WCB714X7pU6jkDTleH5g07jfVEiJfGkn96xT8E/342+VUUxFEyP\nRey6OPW/D4MP4t+Wd8zZ5pJLCqms/Dv8/i8mb1qWJUuuRKfgfFEl52436qkv3uQ6N6k4PlMILoza\nGFn7pHynDdyP6XgWf5GYAdRPVHy/cKEcTf7N0n+vG+cWDcVoOpcjpOB6SSfnZ4lfciPSR5cuXVHV\nphn527dvZdWqFUSj6XljEiKR3I/pLRIzgGIquFfoKMfT8wFVkrMNnK82Ffr4KvWYA/dTelLPrW53\noL/V9npy50b1zCockcUsy2Lfvo/46KO9LF++tHlZpBBZKQLanrbveeoxB64X07O+hiRnG3y5x9z6\nWHLPrR1woETaPr9yWkGR+3TWUxSFadNKGDJkKIcPf87SpYs4dUrqtIospYHla2epqGJhtLOM1G6S\nnG0QL2r7na7lsIiNSu6ypegYA6Og7fMbfU3Z7KKTUFWVKVNu4uqrR3Pq1CmWLFnM4cOf2x2WSCHl\nqIL7cR3nSq3N6oBZQ4XY6Lbvq/FhBrGJ6blUVJKzDYJ/H8Xo3fqCiI4ziN6c3AvF6mERuSmORcun\nRcttES5P35mLIvEURWHMmHFMnHgjoVCQbdu22h2SSAULvL9w0nW8F/9P3OTN9dDlBi/6+vQc3k2E\nxn+JEBnbspZD7DKDwP3RtM2CMlvbBuZAi9OPh/D83oX2ngPcELsmTuN9qblQGv81gtndwrVWw3EC\njEKLcGmMyMzkzxQX6WfEiGK6dcvnwgsvsjsUkQKuxRre/3KixL94Etf3qOQscFFXE0ztks4UsXKh\nvjqE82UV7V0Vs0fT8lXcdkfWPknONjGGWQR+H7bn5A4I3RsldG8ULKS3LCgs7N3851273qe29gTX\nXjtWllplIdeLWovEfIb2sYr7SSehf8zSWaEKRCcbRCen5zD2V0ly7uzk3iu+xDAMNm9+k9raEzQ0\nNDBp0uTm5VciOzjqzjIhVeYFpo00HW0XQthBVVXKyu7gwgsvYufOHTz77DNEIhG7wxIJFO/b/szl\n2FApQJQuJDkLIVrw+XzMmFFB//6XcvDgAaqqlhAISH3nbBGeHcXo2ToJx642iE6VeSfpQpKzEKIV\np9PJ1KnTGT58JEePHmHDhtftDkkkSPxbJg2/DROZEMO4wCTe1yBUHqX+yZBkhDQi75yFEG1yOBxM\nnHgjPXv2ZODAwXaHIxIoNu5vW8GaNM07kbknaUeScwbT3nagb1Ix+phNMxDlqVckmKIojBhR3Pzz\n/v0fcfy4i4KCS2yMSjg+UvA8paOccmD2Ngn9INqxAkJyz0hbkpwzUQhyf+RGf03DEVKaJnIUGzT8\nOow5OD1L0YnMF4vFeOmlF1GUOFdeOYZRo75ld0idkutPKr6fuVGPfWmHpec06v8Ywhwo3/9sIc9N\nGcj3v124XtBxhJrGohRLwblNw7/ADfLdFEmi6zrTp5fi8/lYv34dNTXrsSy54FIqBp7/62qRmAH0\nD1R8v5Rd5bKJJOdMY4BzQ9vrTvVtKvqf5Z9UJE/Pnhdw5513kp+fz1tvbWHNmtXE4zLDN1X0tSp6\nOzss6dtUsKmukUg8uZNnmggo9e3sKhVXcBySf1KRXF26dKGiopKLL76E3bt38frr6+0OqdNoq7JX\nM4OmCV4iK8idPNN4wOjfzq5S+Sax8ZlRmk5kNo/HQ0lJGaNGXcFVV422O5xOIzopTrxvOzssjTDA\nm+KARNJIcs40CoRnxjC/sj+pRdNuU2YveQcoUkPXdW64YSI5OTkAfPbZpxw7dszmqLKcB0Jzo5j+\nlt9zo9Ag+E9ZWhO7k5LZ2hkoUhYHPYRriY520IGZD9HvxAn+s3w5hT3C4TArV67ANA1uu+12evfu\nY3dIWSv8/TjxoiDu5TqOkwrGJSahH8Yw2ynLKTKTYqXJdMvjx7OzPGBBgT9r/9/SibRz6rTX1rt2\nvc9LL60BYPLkmxg8eEiqQ8s62XJdK0cVnK+omL1MYtebaVn0xI62Lihof39O6TkLIRJi8OAh+Hw+\nVq9eyZo1q6mvr+fKK6+SbSc7Mwt8/8uFa5WGetyB5bCIjTQI/GsYY0Ra9AvTlrxzFkIkTO/efSgr\nm4nfn8vGjTVs2bLZ7pCEjdy/0/H8UUc93pRqFPNvNRnu8UDM5uDSnCRnIURC9ejRg5kzK+nTpy+D\nBklN7nSgbXXg/Rcn3vudqO+lbiTDtVZDsVqfT9+p4npWBm7PRlpHCJFwfn8upaXlzT+fOHECr9eL\n1ytrfVLKAt99LjzLdJRwU5L0POEkNCdK8GfJn0DqqG3/QcDxmfQNz0ZaRwiRVI2NjVRXV7F06SLq\n6k7ZHU6n4lyp4Vn0RWIGcDQqeP/LiV7TdqWxRDL6tF2TwXJaxEdJTYazkeQshEgqr9fLoEGDOXny\nJEuWLObIkcN2h9RpuF7RUIzWvVclouB6PvkDp+GZMczc1gk6eu3ftqwU7ZLkLIRIKkVRuO668UyY\nMJFgsJGqqiXs3/+R3WF1CkrkLAejyX/3HJ1iEPi3MNGr4xj5JvHeBqE7otQ/FkrL5VTpRN45CyFS\norj4CnJy/KxZs5qVK1cwZcrNtq6F1t5y4F6q4zihYPQyCc2OYRZl1/Ke+OUmrhfbOTYiNT3XyFSD\nyNQQBAEnknW+Juk5CyFSpqjoMmbMqCAvL4+Cgh62xeGq0si7w4NniRPXWh3vEy66lHrQNib/PWwq\nBedGiY5qvWtY9No44coUr2XyIon5G5CmEkKkVK9eFzNnzt/jcDT1DQKBBrxeX/PPSRcDz6NOHHUt\nz6d+ruJ9RKd+bBa9C82B+qUhPP/uRH9bBQVi3zII3h1t6sWKtCXJWQiRcmcScTAYpKpqCV26dOWW\nW6bidCY/Y+hvOtrfE/ltFeWEgtU9e4a3ra4Q/IXU3c80MqwthLCNqqrk5XVh//59VFUtIRAIJP+k\nOlhKO8nXAajZk5hF5pLkLISwjcvlYtq0EoYOHc6RI4dZunQRJ0/WJvWcsatN4pe3vf42doWB1TWp\npxfia5HkLISwlaqq3HjjFEaPHkNdXR1Llizm888/S94JHRD8cQSjZ8sEHe9nEFxwtrVHQqSOvHMW\nQthOURRGjx6D3++npmY9yd7JNjrFoG5wEPd/6ziOOzAvMQndGcXqntTTCvG1SXIWQqSNYcNGcOml\nRc01uGOxGLquJ+VcZh+L4EKZKCXSkyRnIbKJBa7lGs5XNJRGiA8yCf0ohtUjcyY5nUnMkUiEqqol\n9OnTl7Fjr5N9oUWnIslZiCzi+6kLz3/rzfWUXTXgfF2jfnEI85LMSdAAkUiYWCzKli2baWhoYPLk\n76Kq2VUkRIj2yIQwkTaU4+D7uZO8qR5yZ7jx/EaH1sWNkiMO7kU6OT9ykzPPhXOVBpmVy1B3Krir\n9FYbHei7VHLmu9DXqqlrzwTIzc2joqKSiy7qxa5dO1mxYjnhcNjusIRICek5C3sFQIkBccgr86K/\n90XPyFWjo72r0vDHcHKL5Mcgd7Yb19ov3m26V1iEa2IE/iOSMQX6XS/oOBrbDtb1Zx3nnzXig02C\n/zNCdEpmVMHyer3MmFHBmjWr2bv3Q5Yte5rp00vx+3PtDk2IpJKes7CF46CC//tuul3po9u3fXSd\n0DIxn+F6UcP5SnKHMj2P6y0SM4BiKrirdZwvZs4wqnWOR20FpakXfZ8bx2cZ8sQB6LrOrbdOY+TI\nYmprT1Bbm9x10NlI2+ogZ76L3DI3OXe70N6RW3+6k38hkXoRyL3TjfsFHfW4A8dpB+rhtpOgElfQ\nNyQ3Qeqb2zm3oeBcnzmDS5GyGEa3totrfJl6xIH7ieTMgE4Wh8PBhAmTqKycTZ8+fQGSvtwqW7hW\nqeTO9OBZ6sT1mo5niZPcOzw4X8icB8/OSJKzSDn3Yh19x9dPepYricHA2d8tZ9D93+xlEZoXxcw5\nd9CO2szpOZ+hKAo9ejTtZBWPx6murmLPnt02R5XmTPD8zoV68iubfBx34P2tM6Ou785GkrNIOXX/\n108MZo5FZHpyt7aLXdn2+1dLsYhel0EzqIDQvBh1q4IEfxAhdmn775WNvpl9V66treXw4c957rlV\nvPXWFrvDSVvqbgfae23f5rV3VRwHM+8hrbOQ5CxSzjxLFSbrS4/yZo5F8H9EMIYkJ5EodeD5DyfK\ncYXY0JZJ2MIiMjVO9ObMmDj1ZcZwk8b/E6X+8RDxXq3jjw8yCM3J7OIbPXv2pLx8Fjk5TRXFXntt\nnQxzt0WzoL3Raw3IrLcbnUrmvFATWSM8O4p7mYZ2qOVdw3RbhO6MokTAckLk9hjG5cm54TrXqOT8\n3IX6aVMMlsMiNiCOUWSBE6Lj4kTK4hn9+GoOsmh4JIL3t02z3tGa9vJt/GkEcuyO7vz16NGDmTMr\nqa5eztatb9HQ0MB3v3sLmia3tTOMIotYsYHzr63bJHaFgXmxPNCkK7mKRcpZXaDh1xFyHnCi7VBR\nTIV4H4PQ38UI/yi5Q9gABMF3/xeJGZpmZ+t7NWLjIzTen9m9yi+LjzGoH2NAgKYelMfuiBKraS30\nLFavXskHH+xh6NDh9OvX3+6w0ocCjQuiqPMV1E++uN7jfQ0aZZOPtCbJWdgiPtag7uUQ+iYH1CnE\nxhvgTc253ct1tANtj/Xpb2pA9iTnZlnQU26Px+Nh+vQZHDp0QBJzG+JjDE69FMLzuI7jsNI0cXCO\nbPKR7iQ5C/s4IHbtuZf+JJpS3/4kGCWYwkBEwmiaRv/+AwAwTZN169YyYkQxPXv2tDmy9GD1sAj+\nJAsfOrNYBr9RE6JjIpNimP6237XFB6f+YUEk1ieffMyOHe9QVfU0Bw8esDscITrkvJLzunXr+PGP\nf9zmsWeeeYZp06ZRWlpKTU3N+ZxGiIQyB1qEb4u1mBkOEO9lELpLeheZrnfvPtx8820YhsGKFcvZ\nufM9u0MS4hvr8LD2Aw88wBtvvMGgQYNaHTt+/DiLFy/m2WefJRKJUFFRwejRo3E6necVrBCJ0vhv\nEYxLTZyvqjjqHcQHGIR/GCU+QmavZoOBAwfh8/lYtWoFL774PIFAA1deebVsOykyRod7zsXFxSxc\nuLDNYzt27GDkyJE4nU78fj+FhYXs2bOno6cSIvEcEL4rRv2zYerWBQk8GpHEnGUuuaSQiopKcnNz\n2bjxdT799BO7QxLiaztnz7m6upqnnnqqxWcPPvggU6ZMYcuWtivzBAIB/H5/888+n49AIHDW83Tt\n6kXTsrPWa0GB/9y/JM6btHPqZEpbFxT4mT9/Hrt376a4eIjd4XRIprR1Nkintj5nci4pKaGkpOQb\n/aU5OTk0NjY2/9zY2NgiWbfl1KnsnCZbUODn+PEGu8PIetLOqZOJbd237yCOH2/Asiy2bNnM0KHD\n8fl8dod1TpnY1pnKjrY+28NAUmZrDxs2jG3bthGJRGhoaGDfvn0UFRUl41RCiCRxfKqgb3SgnLI7\nksT58MMP2LjxdZYuXcSpUyftDkeIdiU0OT/55JOsX7+egoICZs2aRUVFBd/73ve4++67cbmSvbWQ\nECIRlDrwz3bT9TovXab76DrWh2+BCzKvzHgrRUWXcdVV13Dq1CmWLFnM4cOf2x2SEG1SrDSpFp+t\nQzcyLJUa0s6J469043659Y4IjT+KEFwYzYq2fued7axbtxZN07jlltuaC5ikm2xo60zRKYa1hRCZ\nyfGBgvPPbU9Fcb2iQQpKn6fCiBHFTJ06HYCVK1dw9OgRmyMSoiUp3ymEaKbvVHE0tr0W2HFUQcmi\nTtyllw5gxowKPvzwA3r0kDKfIr1Iz1kI0Sw2ysDMa7uEqdHLwspLcUBJdtFFvbjuuvHNxUn27NmN\nYWTBy3WR8SQ5CyGamX0souPjrT63FIvILfGmbSez1Pvv7+S551axcmU1kYhspyjsJclZCNFCw79H\nCN0RxbjQwNIs4v0NgvdECf04u+uODxhQRL9+/TlwYD9VVUsIBLJoDF9kHEnOQoiWPBD4fxFOvhnk\n5F8aObUhSHBBFLK8LLXT6WTatBKGDx/J0aNHWLJkEbW1tXaHJTopSc5CiLblgFloQSfar8bhcDBx\n4o1ce+1YTp8+zZIlUqxE2ENmawshOkxpAO8vnehvNS2zig83CM6PYvZJi/IJHaIoCtdccy1+v5+D\nBw/SpUtXu0MSnZAkZyFEx8Qgd5YH56YvbiP6+yradpXTz4SwLsjcBA0wdOhwLr98WPNM7iNHDnPB\nBRfaHJXoLGRYWwjRIe6leovEfIa+R8XzaOsKY5noTGLevXsXixY9yeuvv0aaFFUUWU6SsxCiQ7R3\n2799aHuy69Zy0UUXkZ+fz1//+hfWrFlNPN56uZkQiZRd3yAhRMpY3vZ7kFb6bIubEHl5XSgvn0Wv\nXheze/cuVqxYTjgctjsskcUkOQshOiRcFsPMbV1NzFItopOyr2fp9XopLS2nqOgyPv74EEuXLiYQ\nCNgdlshSkpyFEB1iXG7R+M9RjO5fJGjTbxGaEyNSkn3JGUDXdW65ZSqjRl2Bz+fD4/HYHZLIUjJb\nWwjRYeG5MSJT47iX6RCDyM0xzIHZPWHK4XAwfvx3MAwDVW2qZxoIBMjJybE5MpFNJDkLIc6L1dMi\nND+7S3t+laIoaFrT7XPfvr0899yfmDRpCoMHD7E5MpEtZFhbCCHOg647UVWVNWtWs2XLX2SplUgI\nSc5CCHEeCgt7U1Y2E78/lw0bXmP9+lcwzba33RTi65LkLIQQ56lHjx7MnFlJ9+4FbN++jeeeW0Us\nFrM7LJHBJDkLIUQC+P25VFTMorCwNw0NDTK8Lc6LTAgTQogEcbvdTJ8+g2g0itPZtJ3Xl2d1C/F1\nSc9ZCCESSNM0vF4vAJ988jGPPfafHD16xOaoRKaR5CyEEEly8mQt9fX1LFv2NPv377M7HJFBJDkL\nIUSSDB8+kltvnYZpmqxcWc17771rd0giQ0hyFkKIJCoquozS0nKcThcvvfQCmza9IZPFxDlJchZC\niCS7+OJLuOOOSvLy8ti9e5cssxLnpFjyCCeEEEKkFek5CyGEEGlGkrMQQgiRZiQ5CyGEEGlGkrMQ\nQgiRZiQ5CyGEEGlGkrMQQgiRZmTjiyRYt24dL7/8Mr/+9a9bHXvmmWeoqqpC0zTuuusurr/+ehsi\nzHzhcJh7772X2tpafD4fDz30EN26dWvxO3PnzqWurg5d13G5XDz22GM2RZuZTNNk4cKFfPDBBzid\nTh544AF69+7dfFyu5cQ5V1s/8MADbN++HZ/PB8Cjjz6K3++3K9yM9+677/KrX/2KxYsXt/j8tdde\n43e/+x2apnH77bdTWlpqU4SAJRLq/vvvtyZNmmTNnz+/1bFjx45ZN910kxWJRKz6+vrmP4tv7okn\nnrAeeeQRy7Isa82aNdb999/f6ncmT55smaaZ6tCyxtq1a60FCxZYlmVZb7/9tjV37tzmY3ItJ9bZ\n2tqyLKusrMyqra21I7Ss84c//MG66aabrJKSkhafR6NRa8KECVZdXZ0ViUSsadOmWceOHbMpSsuS\nYe0EKy4uZuHChW0e27FjByNHjsTpdOL3+yksLGTPnj2pDTBLbNu2jTFjxgAwduxYNm/e3OL4iRMn\nqK+vZ+7cuZSXl1NTU2NHmBnty208YsQIdu7c2XxMruXEOltbm6bJoUOH+PnPf05ZWRkrVqywK8ys\nUFhYyG9+85tWNjtPKQAAAo1JREFUn+/bt4/CwkLy8vJwOp2MGjWKrVu32hBhExnW7qDq6mqeeuqp\nFp89+OCDTJkyhS1btrT53wQCgRZDUT6fj0AgkNQ4s0FbbZ2fn9/clj6fj4aGhhbHY7EYs2fPprKy\nktOnT1NeXs6wYcPIz89PWdyZLhAIkJOT0/yzqqrE43E0TZNrOcHO1tbBYJCZM2fy/e9/H8MwqKys\n5PLLL2fgwIE2Rpy5Jk2axKefftrq83S7piU5d1BJSQklJSXf6L/JycmhsbGx+efGxkZ5b/Q1tNXW\n8+bNa27LxsZGcnNzWxzv3r07ZWVlaJpGfn4+gwYN4sCBA5Kcv4GvXq+maaJpWpvH5Fo+P2dra4/H\nQ2VlJR6PB4CrrrqKPXv2SHJOsHS7pmVYO4WGDRvGtm3biEQiNDQ0sG/fPoqKiuwOKyMVFxezYcMG\nADZu3MioUaNaHN+0aRPz588Hmr5ke/fupV+/fimPM5MVFxezceNGAN55550W16pcy4l1trY+ePAg\nFRUVGIZBLBZj+/btDBkyxK5Qs1b//v05dOgQdXV1RKNRtm7dysiRI22LR3rOKfDkk09SWFjIDTfc\nwKxZs6ioqMCyLO6++25cLpfd4WWk8vJyFixYQHl5ObquN8+Mf/jhh7nxxhsZN24cb7zxBqWlpTgc\nDu65555Ws7nF2X3nO9/hzTffpKysDMuyePDBB+VaTpJztfXNN99MaWkpuq5z6623MmDAALtDzhrP\nP/88wWCQGTNmcN999zFnzhwsy+L222+nZ8+etsUlu1IJIYQQaUaGtYUQQog0I8lZCCGESDOSnIUQ\nQog0I8lZCCGESDOSnIUQQog0I8lZCCGESDOSnIUQQog0I8lZCCGESDP/HwGQkZ4o8wc8AAAAAElF\nTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x396 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets.samples_generator import make_circles\n",
    "X, y = make_circles(100, factor=.1, noise=.1)\n",
    "\n",
    "clf = SVC(kernel='linear').fit(X, y)\n",
    "\n",
    "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\n",
    "plot_svc_decision_function(clf);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Clearly, no linear discrimination will ever separate these data.\n",
    "One way we can adjust this is to apply a **kernel**, which is some functional transformation of the input data.\n",
    "\n",
    "For example, one simple model we could use is a **radial basis function**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "r = np.exp(-(X[:, 0] ** 2 + X[:, 1] ** 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we plot this along with our data, we can see the effect of it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "265c0ac3662146bba3e46c21106e7b4f",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "A Jupyter Widget"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits import mplot3d\n",
    "\n",
    "def plot_3D(elev=30, azim=30):\n",
    "    ax = plt.subplot(projection='3d')\n",
    "    ax.scatter3D(X[:, 0], X[:, 1], r, c=y, s=50, cmap='spring')\n",
    "    ax.view_init(elev=elev, azim=azim)\n",
    "    ax.set_xlabel('x')\n",
    "    ax.set_ylabel('y')\n",
    "    ax.set_zlabel('r')\n",
    "\n",
    "interact(plot_3D, elev=(-90, 90), azip=(-180, 180));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that with this additional dimension, the data becomes trivially linearly separable!\n",
    "This is a relatively simple kernel; SVM has a more sophisticated version of this kernel built-in to the process. This is accomplished by using ``kernel='rbf'``, short for *radial basis function*:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAecAAAFJCAYAAAChG+XKAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nzjzzckGrugAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 576x396 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "clf = SVC(kernel='rbf')\n",
    "clf.fit(X, y)\n",
    "\n",
    "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\n",
    "plot_svc_decision_function(clf)\n",
    "plt.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1],\n",
    "            s=200, facecolors='none');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here there are effectively $N$ basis functions: one centered at each point! Through a clever mathematical trick, this computation proceeds very efficiently using the \"Kernel Trick\", without actually constructing the matrix of kernel evaluations.\n",
    "\n",
    "We'll leave SVMs for the time being and take a look at another classification algorithm: Random Forests."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [default]",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
